   Chapter 11.1, Problem 48E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# pH level The pH of a solution is given by pH = -log  [ H + ] where [ H + ] is the concentration of hydrogen ions (in gram atoms per liter). What is the rate of change of pH with respect to [ H + ] ?

To determine

To calculate: The rate of change of [H+] with respect to [H+] where pH=log[H+].

Explanation

Given Information:

The pH of the solution is given by,

pH=log[H+]

Where [H+] is the concentration of hydrogen ions in gram atoms per litre.

Formula Used:

The change of base logax:

logax=lnxlna

The differentiation of logarithmic:

ddx(lnx)=1x

Calculation:

Consider the provided function pH=log[H+].

Rewrite the function in natural logarithmic form,

pH=log[H+]=ln[H+]ln10

Differentiate both sides of above function with respect to pH

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